Such a shaving apparatus is known from U.S. Pat. No. 4,926,550. The lamellae of the external shaving member of the known apparatus are flat. In order to ensure that the hairs are effectively caught in the hair-entry apertures it is very important that the ends of the lamellae have a rounding of a suitable radius. In practice, it has been found that in shavers in accordance with U.S. Pat. No. 4,926,550 the rounding radius should not exceed 0.7 mm. Another important factor is the shaving sensation, i.e. the extent to which the shaver feels rough to the skin. The shaving sensation is influenced by the magnitude of said rounding radius. In practice, a rounding radius of 0.3-0.7 mm is found to be favorable with a view to the shaving sensation. A smaller radius gives an increased sensation of roughness.